It looked like Sven-Goran Eriksson would suffer his first home league defeat as Leicester boss when a header from former Fox Max Gradel and Robert Snodgrass' stunning strike put Leeds in control.
However, Paul Gallacher reduced the hosts' arrears from the penalty spot before Andy King equalised soon afterwards midway through the second half.
The result extended Leeds' unbeaten run to 10 Championship matches but saw the Yorkshire club replaced in second spot by Cardiff.
Leicester, who had already beaten Leeds twice this season in league and cup games at Elland Road, started brightly.
Neill Collins hacked a clearance inside his own area that almost let in King before Steve Howard shot just wide. Richie Wellens was also denied by some good defending from the recalled Andy O'Brien.
Until Gradel scored, Leeds' only noteworthy contribution was the third-minute booking of Luciano Becchio for dissent.
However, Davies and Kyle Naughton were caught napping at the back and a slip from the latter allowed former Foxes trainee Gradel to head home Neil Kilkenny's cross from the right.
The goal saw Leeds grow in confidence and they enjoyed some pressure with a succession of corners.
Leicester responded on the half-hour mark as Kasper Schmeichel reacted well to deny Howard a goal scoring chance.
Howard also sent a long-range effort way over the crossbar after 36 minutes - his attempt perhaps a sign of frustration at the lack of service he and strike partner Darius Vassell had received during the first half.
Howard then joined Becchio in the referee's notebook and headed a chance wide just before the break.
A decisive interception from O'Brien denied Leicester an opportunity as Eriksson's side started brightly again, but Snodgrass extended Leeds' lead with an extraordinary strike in the 55th minute.
Snodgrass' corner was headed back to him and the midfielder hit a first-time shot with the outside of his foot from the narrowest of angles that flew past Chris Kirkland.
Leeds were coasting and could have gone further ahead through Gradel and Snodgrass.
However, the game changed in the 72nd minute when they surrendered possession in midfield and Vassell raced through on goal.
The striker was brought down by Schmeichel, who was lucky to escape with just a yellow card, and Gallacher scored from the spot.
Four minutes later and Leicester were level. King controlled a ball over the top and smashed a 25-yard shot in off the underside of the crossbar.
Leeds had two chances to snatch victory late on, both from corners. Kirkland saved from Collins before the ball was hacked clear and Billy Paynter also had a shot cleared off the line.